A consideration on the condition number of extremely ill-conditioned matrices

As for a matrix A we examine two problems: (a) To find the upper and the lower bound of Cond
₂
(A) in terms of two coefficients p
₁
and p
_n-1
(see Section 2) of the characteristic polynomial of AA
^T
, and (b) proof of existence of a matrix A having considerably larger condition number than that obtained in the previous papers. The connection between (a) and (b) is illustrated.